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I argue that the field equations of any theory of gravity which isdiffeomorphism invariant must be expressible as a thermodynamic identity,TdS=dE around any event in the spacetime. This fact can be demonstratedexplicitly (and rather easily) if: (a) one accepts the Noether current of thetheory as providing the definition for local entropy density and (b) one isallowed to introduce the local notions of a Rindler frame, acceleration horizonand a Killing vector (related to translation in Rindler time) around any event.It is conceptually incorrect - in general - to invert this argument and obtainthe field equations of the theory from the thermodynamic identity. I discussunder what conditions this may be possible. Several subtleties related to thesearguments are described.

Entropy density of spacetime and thermodynamic interpretation of field equations of gravity in any diffeomorphism invariant theory